Police in New Canaan, Connecticut -- a suburb of New York -- said they went to Simon's home on Saturday night to "investigate a family dispute."
The 72-year-old Simon and the 48-year-old Brickell were arrested and released. Both are expected to appear before a judge today.
Simon is a 12-time Grammy winner who shot to stardom as half of the duo Simon and Garfunkel, which produced hits like "Bridge Over Troubled Water" and "Mrs. Robinson."
Brickell, a folk rock singer born in Texas, married Simon in 1992. The couple has three children.